Question
Divide to find the quotient of 78÷[4 1/5 ]. Simplify the answer, if possible.
5/24
3 27/40
40/147
4 4/5
5/24
3 27/40
40/147
4 4/5
Answers
GPT 3.5
To divide 78 by 4 1/5, we first need to convert the mixed number to an improper fraction:
4 1/5 = (4*5 + 1) / 5 = 21/5
Now, we can divide 78 by 21/5:
78 ÷ (21/5)
To divide by a fraction, we can multiply by its reciprocal:
78 * (5/21)
The 21 cancels out in the numerator and denominator, leaving us with:
78 * (5/21) = (78*5)/21 = 390/21
Simplifying the fraction, we find that the quotient is:
390/21 = 18 12/21
To simplify further, we can divide both the numerator and denominator by the greatest common divisor of 390 and 21, which is 3:
390/21 = (390/3)/(21/3) = 130/7
Therefore, the simplified quotient of 78 ÷ (4 1/5) is:
130/7
4 1/5 = (4*5 + 1) / 5 = 21/5
Now, we can divide 78 by 21/5:
78 ÷ (21/5)
To divide by a fraction, we can multiply by its reciprocal:
78 * (5/21)
The 21 cancels out in the numerator and denominator, leaving us with:
78 * (5/21) = (78*5)/21 = 390/21
Simplifying the fraction, we find that the quotient is:
390/21 = 18 12/21
To simplify further, we can divide both the numerator and denominator by the greatest common divisor of 390 and 21, which is 3:
390/21 = (390/3)/(21/3) = 130/7
Therefore, the simplified quotient of 78 ÷ (4 1/5) is:
130/7